Question

the greatest 3 digit number which is divisible by 18 , 24 , 32​

Answer 1

The greatest 3-digit number which is divisible by 18, 24 and 32 is 864.

Given data:

The three numbers 18, 24 and 32

To find:

The greatest 3-digit number which is divisible by 18, 24 and 32

Concept to be used:

In order to find the number divisible by two or more numbers, we have to find their LCM.

Step-by-step explanation:

Here, 18 = 2 × 3 × 3,

24 = 2 × 2 × 2 × 3 and

32 = 2 × 2 × 2 × 2 × 2

Then LCM

= 2 × 2 × 2 × 2 × 2 × 3 × 3

= 288, which is exactly divisible by 18, 24 and 32 but this is not certainly the greatest

We multiply 288 by 2, 3, ... and stop when we get a number > 999.

288 × 2 = 576

288 × 3 = 864

288 × 4 = 1152 > 999

So, 864 is the required 3-digit number.

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